a 
Theorem for Irreversible Cyeles. DAG. 
when not undergoing changes of form the stress at any point 
across a plane is wholly normal we deduce that in a fluid at 
rest the stresses across all planes through a given pointare at 
that point of the same intensity, and accordingly to the value 
of this stress we give, and are justified in giving, the name 
“pressure at the given point.” But in the case of an actual 
fluid whose parts are in relative motion, itis no longer the case 
that the stress across every plane is normal: this is only true for 
the fictitious ideal “perfect fluid,” which we define as having 
this property; (a “perfect gas ” as usually defined is not, and 
indeed according to the kinetic theory a gas cannot be, a 
“verfect fluid’). According to any of the various theories 
of stress in a fluid whose parts are in relative motion which 
have been constructed by O. E. Meyer, Navier, Poisson, 
St. Venant, Stokes, and others, through a given point there 
can be drawn three, and in general only three, planes such 
that at that point the stress across each is normal; the arith- 
metical mean of these three stresses, which are in general 
unequal, is what in such cases is conventionally called “the 
pressure at the given point.” Furthermore, whether this. 
“pressure ”’ is the same as if the fluid in the neighbourhood 
of the point were in a state of equilibrium at the same 
temperature and density, is a question whose answer, in the 
case of a gas.at all events, is doubtfal*, and even whose 
meaning, owing to the difficulty of defining temperature 
in such cases, is not absolutely clear. At all events Planck 
apparently requires each small portion of a fluid to be 
passed, by means of a process at every stage of which the 
stresses exerted on it across its surface are wholly perpen- 
dicular to that surface, out of a state in which some of those 
stresses are oblique, and in the case of a highly viscous fluid 
may be very much so. The argument seems to involve an 
absolute contradiction in terms, and its validity can scarcely 
be admitted without further justification. The difficulty of 
course cannot be got over by the consideration of a more 
general stress-system such as exists ina perfectly elastic solid. 
* The question is the same as whether in a fluid expanding uniformly in 
all directions, this being the only case in which the stresses across all planes 
are normal, the pressure depends only on the density and temperatureat the 
instant, and not on the rate of expansion. Stokes (“On the Friction of 
Fluids in Motion, &c.,” Camb. Phil. Trans. viii.; Math. and Phys. Papers, 
vol. 1.) answers this question in the affirmative ; Meyer (Kinetische Theorie 
der Gase, or Baynes’ translation) in the negative. Lord Rayleigh, while 
adopting the view of Stokes in his ‘Theory of Sound,’ vol. ii. chap. xix., 
appears more recently to doubt its correctness, in a paper “ On the Cooling 
of Air by Radiation and Conduction, &c.” (Phil. Mag. vol. xlvii.; 
Collected Papers, vol. iv.). 
